Problem: Solve for $x$ and $y$ using elimination. ${6x+3y = 78}$ ${-5x-3y = -68}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $3y$ and $-3y$ cancel out. ${x = 10}$ Now that you know ${x = 10}$ , plug it back into $\thinspace {6x+3y = 78}\thinspace$ to find $y$ ${6}{(10)}{ + 3y = 78}$ $60+3y = 78$ $60{-60} + 3y = 78{-60}$ $3y = 18$ $\dfrac{3y}{{3}} = \dfrac{18}{{3}}$ ${y = 6}$ You can also plug ${x = 10}$ into $\thinspace {-5x-3y = -68}\thinspace$ and get the same answer for $y$ : ${-5}{(10)}{ - 3y = -68}$ ${y = 6}$